This relates to apparatus for parallel processing of signals, and in particular, to apparatus for highly parallel computation leading to the decomposition of signals into component signals.
Digital computers are ubiquitous and quite powerful, but that is not to say that digital computers do not exhibit certain limitations in problem solving. Many practical problems, in fact, take such an enormous amount of computation that a solution in real time is not possible. Such difficulties are experienced, for example, in programs that aim to select from memory the information that best satisfies known characteristics or descriptors (which may be referred to as "clues") when the clues are insufficient to completely define the information. Pattern recognition is another example of where the computational problem is just too great for digital computers.
Most artisans either suffer the limitations of general purpose digital computers or develop special purpose digital computers to solve their particular problems more efficiently.
In a copending application entitled "Electronic Network For Collective Decision Based On Large Number Of Connections Between Signals", by J. J. Hopfield, a generalized circuit was disclosed having N amplifiers of high gain and an N.times.N interconnection matrix having N input conductors and N output conductors. The amplifiers exhibit a sigmoid input-output relation, with a minimum and a maximum possible output which can be thought of as a "0" and a "1". Each input conductor of the matrix is connected to the input of a separate one of the amplifiers, and each amplifier has its output terminals (positive and negative) connected to a separate one of the matrix output conductors. Each amplifier has in addition an input capacitance C.sub.i and an input resistance .rho..sub.i. Within the interconnection matrix each input conductor i is connected to an output conductor j through a resistor R.sub.i,j. In the disclosed circuit each amplifier satisfies the circuit equation of motion: ##EQU1## u.sub.i is the input voltage to amplifier i, V.sub.j is the output voltage of an amplifier j, and I.sub.i is the current into the input terminal of amplifier i (e.g., from a high impedance source).
The motion of the disclosed circuit (as specified by the above equation) drives the network to one of a set of predetermined stable states which presents an output pattern of binary 1's and 0's (since the amplifiers have a high gain).
When used for accessing information in a associative memory, the input voltages of amplifiers i are set in correspondence with the individual bits of the input word for each clue (descriptor) known for the information desired. Alternatively, a constant current I.sub.i can be applied to each input in proportion to the confidence that the voltage V.sub.i should be at "1" in the final answer. Once started, the amplifiers drive to a stable state, producing at the output a unique word that represents the information itself, which could include the address of a location in another memory which may then yield a block of words that comprise the information defined by the descriptor used to store and retrieve the unique word from the associative memory.
When used for problem solutions, all inputs may be set approximately equal, such as to zero, or held in a pattern representing input information, and the output pattern of bits "1" and "0" define the solution. In either application, problem solving or information retrieval, the output in binary form is a very good solution to the given problem.
Although the disclosed circuit quickly and efficiently reaches a stable solution state, it is not guaranteed that the optimal solution to a given problem is obtained. This is because the topology of the solution space is very rough, with many local minima, and therefore many good solutions are similar to the optimal solution. In difficult robotics and biological problems of recognition and perception, very good solutions that are rapidly calculated may provide sufficient information to be of practical use, but in some applications it is the exact, or best, solution that is desired.
It is an object of this invention to employ a network of analog processors in connection with decomposition processes.